A Two-Phase Model for Smoothly Joining Disparate Growth Phases in the Macropodid Thylogale billardierii

Abstract

Generally, sigmoid curves are used to describe the growth of animals over their lifetime. However, because growth ratesoften differ over an animal’s lifetime a single curve may not accurately capture the growth. Broken-stick models constrainedto pass through a common point have been proposed to describe the different growth phases, but these are oftenunsatisfactory because essentially there are still two functions that describe the lifetime growth. To provide a single,converged model to age animals with disparate growth phases we developed a smoothly joining two-phase nonlinearfunction (SJ2P), tailored to provide a more accurate description of lifetime growth of the macropod, the Tasmanianpademelon Thylogale billardierii. The model consists of the Verhulst logistic function, which describes pouch-phase growth– joining smoothly to the Brody function, which describes post-pouch growth. Results from the model demonstrate thatmale pademelons grew faster and bigger than females. Our approach provides a practical means of ageing wildpademelons for life history studies but given the high variability of the data used to parametrise the second growth phaseof the model, the accuracy of ageing of post-weaned animals is low: accuracy might be improved with collection oflongitudinal growth data. This study provides a unique, first robust method that can be used to characterise growth overthe lifespan of pademelons. The development of this method is relevant to collecting age-specific vital rates fromcommonly used wildlife management practices to provide crucial insights into the demographic behaviour of animalpopulations

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